Prof. Mark Richard Wilson
|Professor in the Department of Chemistry||CG139||+44 (0) 191 33 42144|
We use classical molecular dynamics and Monte Carlo simulation methods to study problems in soft matter chemistry. We concentrate on materials that are ordered on the nanoscale, including liquid crystals, colloids, polymers, amphiphilic molecules and proteins. A key part of our work involves multiscale simulations of soft matter systems, including developing and testing new coarse-grained models.
Read about our latest simulations at my research group web pages.
We are developing new coarse-grained models for soft matter systems.1 Coarse-grained models allow molecular simulation to be carried out over time scales that are not accessible to conventional atomistic simulations. Long time scales allow us to observe self-assembly in solution, study polymers, observe segregation of molecules to an interface, or see formation of complex molecular structures mediated by specific molecular interactions.
Models to understand dynamic allostery in proteins
Allostery is a process by which a molecule binding to one site of a protein alters the activity of the protein at another site. We have developed new models to help understand how protein dynamics can influence allostery. In cases where the protein undergoes no conformational change on binding a small molecule, we demonstrate that that allostery arises as a natural consequence of changes in global low-frequency protein fluctuations on ligand binding.2
Simulation of chromonic liquid crystals
We have recently carried out the first detailed study of the structure and dynamics of a chromonic liquid crystal (edicol - the food dye sunset yellow).3 The simulations show spontaneous self-assembly in water at atomistic detail, and can be used to determine the free energy of association in solution. Sunset yellow is seen to form single molecule stacks with a preference for head-to-tail ordering, which at higher concentrations form liquid crystal phases in water (as shown in the picture above). Our work shows that simulation can be used to understand, predict and control molecular self-assembly with a view to the future use of chromonic materials for applications in self-assembled molecular electronics.
Dynamics in soft solids
We have been using atomistic simulation to study dynamics in molecular solids.4 Our recent work with octafluoronaphthalene and urea inclusion compounds has indicated that its is now possible to look at dynamical processes over tens of ns, and study correlated motion in solids. This provides the possiblity of using simulation to complement and help interpret experimental solid state NMR data, and raises intriguing questions as to whether we can use simulation to help engineer tractable molecular machines for future applications.
Simulation of liquid crystal molecules and calculation of material properties
Molecular simulations provide a way of understanding the structure and dynamics5 of complex materials such as liquid crystals. We have recently used6 atomistic simulation to study the structure of the first low molecular weight biaxial nematic liquid crystal, ODBP-Ph-C7.
We have also been developing techniques to simulate liquid crystal molecules at the atomistic level and predict material properties in liquid crystal phases from simulation. For example, the rotational viscosity determines how quickly a nematic liquid crystal can reorientate in a liquid crystal display; and can be determined from our simulations by monitoring the liquid crystal director in the course of a molecular dynamics simulation.7 To carry out this work, we need accurate representations of intramolecular interactions within a molecule and intermolecular interactions between molecules. This is made possible by a new force field for use in materials chemistry, which we have been developing.8
The picture shows a sequence of time frames showing the slow growth of a biaxial phase from a uniaxial starting point. As the phase grows it develops ferroelectric domains, which are shown colour-coded. Molecules which are blue and red have transverse dipoles pointing in opposite directions.
A snapshot from a molecular dynamics simulation showing the liquid crystal molecule PCH5 in a nematic phase.
Simulation studies of amphiphilic molecules in water
We are interested in the properties of amphiphilic molecules and have used simulation to understand the behaviour of amphiphilic polymers at a water/air interface. The simulations can be used to interpret the results of complementary neutron diffraction studies by calculating neutron reflectivity curves to match with experiment.9
Similar modelling techniques are being used to study lipid - amino acid interactions. Our recent atomistic work in this area seeks to understand how these interactions (specifically the balance of hydrogen bonding and cation-Pi interactions) can be perturbed by small chemical modifications of the amino acid structure. Such studies seek to aid our understanding of binding between proteins and cell membranes.
Snapshots from a simulation study of an amphiphilic polymer at a water-air interface at low surface concentration. The hydrophobic polynorbornene backbone is shown in blue and the hydrophilic poly(ethylene oxide) (PEO) grafts are shown in red. The dots represent water molecules. At higher surface concentrations the PEO chains are forced down into the aqueous subphase to form a polymer brush.
Coarse-grained models for the simulation of polymers, dendrimers, liquid crystals and lipids
We have developed new coarse-grained models to study the bulk structure of liquid crystalline polymers and dendrimers10 and are working on “molecular engineering” tools to design molecules to have the desired organisation at the nanoscale. This research is being extended to lipid bilayers and vesicles. An important part of our work has involved developing efficient simulation methods that make use of parallel computers, so we are able to simulate extremely large systems composed of many molecules and take advantage of today’s supercomputers.11
The figure shows microphase separation in a liquid crystalline side chain polymer to give polymer-rich and liquid crystal-rich regions. Blue: polymer backbone (methylsiloxane), white: liquid crystal group, red: flexible spacer groups (alkyl chain).
More on Soft Matter Simulations
Read about our latest simulations at my research group web pages
- Prasitnok K., and Wilson M. R. A coarse-grained model for polyethylene glycol in bulk water and at a water/air interface. Phys. Chem. Chem. Phys., 2013, 15, 17093-1710.
- Rodgers T. L., Townsend P. D., Burnell D., Jones M. L., Richards S. A., McLeish T. C. B., Pohl E., Wilson M. R., Cann M. J. Modulation of Global Low-Frequency Motions Underlies Allosteric Regulation: Demonstration in CRP/FNR Family Transcription Factors. PLoS Biol, 2013, 11(9): e1001651.
- Chami F. and Wilson M. R. Molecular Order in a Chromonic Liquid Crystal: A Molecular Simulation Study of the Anionic Azo Dye Sunset Yellow. J. Am. Chem. Soc., 2010, 132, 7794.
- Ilott A. J., Palucha S., Batsanov A. S., Wilson M. R. and Hodgkinson P. Elucidation of Structure and Dynamics in Solid Octafluoronaphthalene from Combined NMR, Diffraction, And Molecular Dynamics Studies. J. Am. Chem. Soc., 2010, 132, 5179.
- Oganesyan, V. S., Kuprusevicius, E., Gopee, H., Cammidge, A. N., Wilson, M. R. Simulation of EPR spectra directly from molecular dynamics trajectories of a liquid crystal with doped paramagnetic spin probe. Phys. Rev. Lett., 2009, 102, 013005(1)-013005(4).
- Pelaez J. and Wilson M. R. Atomistic Simulations of a Thermotropic Biaxial Liquid Crystal. Phys. Rev. Lett., 2006, 97., 267801.
- Cheung D. L., Clark S. J, Wilson M. R. Calculation of the rotational viscosity of a nematic liquid crystal. Chem. Phys. Lett., 2002, 356, 140.
- Cheung D. L., Clark S. J., Wilson M. R. Parametrization and validation of a force field for liquid-crystal forming molecules. Phys. Rev. E, 2002, 65,051709.
- Anderson P. M. and Wilson M. R. Molecular Dynamics Simulations of an Amphiphilic Graft Copolymer at a Water/Air Interface., 2004, J. Chem. Phys, 121, 8503.
- Wilson M. R., Ilnytskyi J. M., Stimson L. M., Computer simulations of a liquid crystalline dendrimer in liquid crystalline solvents. J. Chem. Phys., 2003, 119, 3509.
- Ilnytskyi J, Wilson M. R.. A domain decomposition molecular dynamics program for the simulation of flexible molecules with an arbitrary topology of Lennard-Jones and/or Gay-Berne sites. Comput. Phys. Comm., 2001, 134, 23.
- Earl D. J., M., Wilson M. R. Predictions of molecular chirality and helical twisting powers: A theoretical study. J. Chem. Phys., 2003, 119, 10280.
- Theoretical and Computational Chemistry
- Soft Matter
- Liquid Crystals and Polymers
- Computational and Dynamics
- Soft Matter and Interfaces
- 2017: Small Molecule migration in, on and through complex formulations: Towards predictive control and sustainable future(£426516.80 from Engineering and Physical Sciences Research Council)
Chapter in book
- M.R. Wilson (2001). Calculations of nematic mesophase properties using realistic potentials. In Physical properties of liquid crystals: nematics. D. Dunmur, A. Fukada & G. Luckhurst Institution of Electrical engineers, England 2001. 635-643.
- Wilson, Mark Richard, Yu, Gary, Potter, Thomas D., Walker, Martin, Gray, Sarah Jane, Li, Jing & Boyd, Nicola Jane (2022). Molecular simulation approaches to the study of thermotropic and lyotropic liquid crystals. Crystals 12(5): 685.
- Yu, Gary & Wilson, Mark Richard (2022). All-atom simulations of bent liquid crystal dimers: the twist-bend nematic phase and insights into conformational chirality. Soft Matter 18(15): 3087-3096.
- Gary, Yu & Wilson, Mark Richard (2022). Molecular simulation studies of self-assembly for a chromonic perylene dye: all-atom studies and new approaches to coarse-graining. Journal of Molecular Liquids 345: 118210.
- Patyukova, Elena Xi, Erte & Wilson, Mark (2021). Phase behavior of correlated random copolymers. Macromolecules 54(6): 2763-2773.
- Yu, Gary Walker Martin & Wilson, Mark R. (2021). Atomistic simulation studies of ionic cyanine dyes: self-assembly and aggregate formation in aqueous solution. Physical Chemistry Chemical Physics 23(11): 6408-6421.
- Potter, Thomas D., Walker, Martin & Wilson, Mark R. (2020). Self-assembly and mesophase formation in a non-ionic chromonic liquid crystal: insights from bottom-up and top-down coarse-grained simulation models. Soft Matter 16(41): 9488-9498.
- Tasche, Jos Sabattie, Elise F. D. Thompson, Richard L. Campana, Mario & Wilson, Mark R. (2020). Oligomer/polymer blend phase diagram and surface concentration profiles for squalane/polybutadiene: experimental measurements and predictions from SAFT-g Mie and molecular dynamics simulations. Macromolecules 53(7): 2299-2309.
- Shadpour, Sasan Nemati, Ahlam Salamończyk, Mirosław Prévôt, Marianne E. Liu, Jiao Boyd, Nicola J. Wilson, Mark R. Zhu, Chenhui Hegmann, Elda Jákli, Antal I. & Hegmann, Torsten (2020). Missing Link between Helical Nano‐ and Microfilaments in B4 Phase Bent‐Core Liquid Crystals, and Deciphering which Chiral Center Controls the Filament Handedness. Small 16(4): 1905591.
- Mensa-Bonsu, Golda, Wilson, Mark R., Tozer, David J. & Verlet, Jan R. R. (2019). Photoelectron spectroscopy of para-benzoquinone cluster anions. The Journal of Chemical Physics 151(20): 204302.
- Shadpour,Sasan, Nemati,Ahlam, Boyd,Nicola Jane, Li,Lin, Prevot, Marianne Estelle, Wakerlin, Samantha L., Vanegas,Julie P. Salamonczyk, Mirosław, Hegmann, Elda, Zhu,Chenhui Wilson, Mark R., Jakli, Antal I. & Hegmann,Torsten (2019). Heliconical-layered nanocylinders (HLNCs) –hierarchical self-assembly in a unique B4 phase liquid crystal morphology. Materials Horizons 6(5): 959-968.
- Potter, Thomas D. Tasche, Jos & Wilson, Mark R. (2019). Assessing the transferability of common top-down and bottom-up coarse-grained molecular models for molecular mixtures. Physical Chemistry Chemical Physics 21(4): 1912-1927.
- Thind, Romnik, Walker, Martin & Wilson, Mark R. (2018). Molecular simulation studies of cyanine-based chromonic mesogens: spontaneous symmetry breaking to form chiral aggregates and the formation of a novel lamellar structure. Advanced Theory and Simulations 1(10): 1800088.
- Lintuvuori, Juho S., Yu, Gary, Walker, Martin & Wilson, Mark R. (2018). Emergent chirality in achiral liquid crystals: insights from molecular simulation models of the behaviour of bent-core mesogens. Liquid Crystals 45(13-15): 1996-2009.
- Catte, Andrea, White, Gaye F., Wilson, Mark R. & Oganesyan, Vasily S. (2018). Direct Prediction of EPR Spectra from Lipid Bilayers: Understanding Structure and Dynamics in Biological Membranes. ChemPhysChem 19(17): 2183-2193.
- Catte, Andrea, Wilson, Mark R., Walker, Martin & Oganesyan, Vasily S. (2018). Antimicrobial action of the cationic peptide, chrysophsin-3: a coarse-grained molecular dynamics study. Soft Matter 14(15): 2796-2807.
- Kim, Byeong-Cheon, Walker, Martin, Jo, Seong-Yong, Wilson, Mark R., Takezoe, Hideo & Choi, Suk-Won (2018). Effect of terminal chain length on the helical twisting power in achiral bent-core molecules doped in a cholesteric liquid crystal. RSC Advances 8(3): 1292-1295
- Boyd, Nicola Jane & Wilson, Mark Richard (2018). Validating an optimized GAFF force field for liquid crystals: TNI predictions for bent-core mesogens and the first atomistic predictions of a dark conglomerate phase. Physical Chemistry Chemical Physics 20(3): 1485-1496.
- Potter, Thomas D., Tasche, Jos, Barrett, Elin L., Walker, Martin & Wilson, Mark R. (2017). Development of new coarse-grained models for chromonic liquid crystals: insights from top-down approaches. Liquid Crystals 44(12-13): 1979-1989.
- Güryel, S., Walker, M., Geerlings, P., De Proft, F. & Wilson, M. R. (2017). Molecular dynamics simulations of the structure and the morphology of graphene/polymer nanocomposites. Physical Chemistry Chemical Physics 19: 12959-12969.
- Sabattié, Elise, Tasche, Jos, Wilson, Mark Richard, Skoda, Maximilian W. A., Hughes, Arwel V., Lindner, Torsten & Thompson, Richard (2017). Predicting Oligomer/Polymer Compatibility and its Impact on Nanoscale Segregation in Thin Films. Soft Matter 13(19): 3580-3591.
- Jo, Seong-Yong, Kim, Byeong-Cheon, Jeon, Sung-Wook, Bae, Jae-Hyun, Walker, Martin, Wilson, Mark, Choi, Suk-Won & Takezoe, Hideo (2017). Enhancement of the helical twisting power with increasing the terminal chain length of nonchiral bent-core molecules doped in a chiral nematic liquid crystal. RSC Advances 7(4): 1932-1935.
- Walker, Martin & Wilson, Mark R. (2016). Simulation insights into the role of antiparallel molecular association in the formation of smectic A phases. Soft Matter 12(43): 8876-8883.
- Walker, Martin & Wilson, Mark R. (2016). Formation of complex self-assembled aggregates in non-ionic chromonics: dimer and trimer columns, layer structures and spontaneous chirality. Soft Matter 12(41): 8588-8594.
- Degiacomi, M.T., Erastova, V. & Wilson, M.R. (2016). Easy creation of polymeric systems for molecular dynamics with Assemble! Computer Physics Communications 202: 304-309.
- Boyd, Nicola Jane & Wilson, Mark Richard (2015). Optimization of the GAFF Force Field to Describe Liquid Crystal Molecules: The Path to a Dramatic Improvement in Transition Temperature Predictions. Physical Chemistry Chemical Physics 17(38): 24851-24865.
- Townsend, P.D., Rodgers, T.L., Glover, L.C., Korhonen, H.J., Richards, S.A., Colwell, L.J., Pohl, E., Wilson, M.R., Hodgson, D.R.W., McLeish, T.C.B. & Cann, M.J. (2015). The role of protein-ligand contacts in allosteric regulation of the Escherichia coli Catabolite Activator Protein. Journal of Biological Chemistry 290(36): 22225-22235.
- Walker, M. & Wilson, M. R. (2015). A simple model for chromonic aggregation. Molecular Crystals and Liquid Crystals 612(1): 117-125.
- Townsend, P.D., Rogers, T.L., Pohl, E., Wilson, M.R., McLeish, T.C.B. & Cann, M.J. (2015). Global low-frequency motions in protein allostery: CAP as a model system. Biophysical Reviews 7(2): 175-182.
- Akinshina, A., Walker, M., Wilson, M. R., Tiddy, G. J. T., Masters, A. J. & Carbone, P. (2015). Thermodynamics of the self-assembly of non-ionic chromonic molecules using atomistic simulations. The case of TP6EO2M in aqueous solution. Soft Matter 11(4): 680-691.
- Walker, M., Masters, A. J. & Wilson, M. R. (2014). Self-assembly and mesophase formation in a non-ionic chromonic liquid crystal system: insights from dissipative particle dynamics simulations. Physical Chemistry Chemical Physics 16(42): 23074-23081.
- Rodgers Thomas L Burnell, David Townsend, Phil D, Pohl, Ehmke, Cann, Martin J, Wilson, Mark R & McLeish, Tom C B (2013). DDPT: a comprehensive toolbox for the analysis of protein motion. BMC Bioinformatics 14(1): 183.
- Rodgers, TL, Townsend, PD, Burnell, D, Jones, ML, Richards, SA, McLeish, TCB, Pohl, E, Wilson, MR & Cann, MJ (2013). Modulation of Global Low-Frequency Motions Underlies Allosteric Regulation: Demonstration in CRP/FNR Family Transcription Factors. PLoS Biology 11(9): e1001651.
- Ilott, Andrew J., Palucha, Sebastian, Hodgkinson, Paul & Wilson, Mark R. (2013). Well-Tempered Metadynamics as a Tool for Characterizing Multi-Component, Crystalline Molecular Machines. Journal of Physical Chemistry B 117(40): 12286-12295.
- Prasitnok, Khongvit & Wilson, Mark R. (2013). A coarse-grained model for polyethylene glycol in bulk water and at a water/air interface. Physical Chemistry Chemical Physics 15(40): 17093-17104.
- McLeish, Thomas C. B., Rodgers, T. L. & Wilson, Mark R. (2013). Allostery without conformation change: modelling protein dynamics at multiple scales. Physical Biology 10(5): 056004.
- Ilott, AJ Palucha, S, Batsanov, AS Harris, KDM Hodgkinson, P & Wilson, MR (2011). Structural Properties of Carboxylic Acid Dimers Confined within the Urea Tunnel Structure: An MD Simulation Study. The Journal of Physical Chemistry B 115(12): 2791–2800.
- Chami, F & Wilson, MR (2010). Molecular Order in a Chromonic Liquid Crystal: A Molecular Simulation Study of the Anionic Azo Dye Sunset Yellow. Journal of the American Chemical Society 132(22): 7794-7802.
- Oganesyan, VS, Kuprusevicius, E, Gopee, H, Cammidge, AN & Wilson, MR (2009). Electron Paramagnetic Resonance Spectra Simulation Directly from Molecular Dynamics Trajectories of a Liquid Crystal with a Doped Paramagnetic Spin Probe. Physical Review Letters 102(1): 013005.
- Lintuvuori, JS & Wilson, MR (2009). A coarse-grained simulation study of mesophase formation in a series of rod–coil multiblock copolymers. Physical Chemistry Chemical Physics 11(12): 2116-2125.
- Duncan, PD, Dennison, M, Masters, AJ & Wilson, MR (2009). Theory and computer simulation for the cubatic phase of cut spheres. Physical Review E 79(3): 031702.
- Pelaez, J. & Wilson, M. R. (2006). Atomistic simulations of a thermotropic biaxial liquid crystal. Physical Review Letters 97(26): 267801.
- Wilson & MR (2005). Progress in computer simulations of liquid crystals. International Reviews in Physical Chemistry 24(3-4): 421-455.
- D. J. Earl, M. A. Osipov, H. Takezoe, Y. Takanishi & M. R. Wilson (2005). Induced and spontaneous deracemization in bent-core liquid crystal phases and in other phases doped with bent-core molecules. Physical Review E 71(2).
- Z. E. Hughes, M. R. Wilson & L. Stimson. (2005). Coarse-grained simulation studies of a liquid crystal dendrimer: towards computational predictions of nanoscale structure through microphase separation. Soft Matter 1(6): 436-443.
- L.M. Stimson & M.R. Wilson (2005). Molecular dynamics simulations of side chain liquid crystal polymer molecules in isotropic and liquid-crystalline melts. Journal of Chemical Physics 123(3): 034908.
- P. M. Anderson & M. R. Wilson (2005). Developing a force field for simulation of poly(ethylene oxide) based upon ab initio calculations of 1,2-dimethoxyethane. Molecular Physics 103(1): 89-97.
- P. M. Anderson & M. R. Wilson (2004). Molecular dynamics simulations of amphiphilic graft copolymer molecules at a water/air interface. Journal of Chemical Physics 121(17): 8503-8510.
- Cheung, D.L., Clark, S.J. & Wilson, M.R. (2004). Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation. Journal of Chemical Physics 121(18): 9131-9139.
- D. J. Earl & M. R. Wilson (2004). Calculations of helical twisting powers from intermolecular torques. Journal of Chemical Physics 120(20): 9679-9683.
- D. J. Earl & M. R. Wilson (2003). Predictions of molecular chirality and helical twisting powers: A theoretical study. Journal of Chemical Physics 119(19): 10280-10288.
- A. F. Miller, M. R. Wilson, M. J. Cook & R. W. Richards (2003). Monte Carlo simulations of an amphiphilic polymer at a hydrophobic/hydrophilic interface. Molecular Physics 101(8): 1131-1138.
- M. R. Wilson, J. M. Ilnytskyi & L. M. Stimson (2003). Computer simulations of a liquid crystalline dendrimer in liquid crystalline solvents. Journal of Chemical Physics 119(6): 3509-3515.
- M. P. Neal, M. Solymosi, M. R. Wilson & D. J. Earl (2003). Helical twisting power and scaled chiral indices. Journal of Chemical Physics 119(6): 3567-3573.
- M. Solymosi, R. J. Low, M. Grayson, M. P. Neal, M. R. Wilson & D. J. Earl (2002). Scaled chiral indices for ferroelectric liquid crystals. Ferroelectrics 277: 483-490.
- A. Cuetos, J. M. Ilnytskyi & M. R. Wilson (2002). Rotational viscosities of Gay-Berne mesogens. Molecular Physics 100(24): 3839-3845.
- Cheung, DL, Clark, SJ & Wilson, MR (2002). Parametrization and validation of a force field for liquid-crystal forming molecules. PHYSICAL REVIEW E 65(5, Part 1): 051709.
- J. M. Ilnytskyi & M. R. Wilson (2002). A domain decomposition molecular dynamics program for the simulation of flexible molecules of spherically-symmetrical and nonspherical sites. II. Extension to NVT and NPT ensembles. Computer Physics Communications 148(1): 43-58.
- Cheung, D.L., Clark, S.J. & Wilson, M.R. (2002). Calculation of the rotational viscosity of a nematic liquid crystal. Chemical Physics Letters 356(1-2): 140-146.
- M.J. CookM.R. Wilson (2001). The first thousand-molecule simulation of a mesogen at the fully atomistic level. Molecular Crystals and Liquid Crystals 363: 181-+.
- M.R. WilsonD.J. Earl (2001). Calculating the helical twisting power of chiral dopants. Journal of Materials Chemistry 11(11): 2672-2677.
- J.M. IlnytskyiM.R. Wilson (2001). Molecular models in computer simulation of liquid crystals. Journal of Molecular Liquids 92(1-2): 21-28.
- J. Ilnytskyi & M. R. Wilson (2001). A domain decomposition molecular dynamics program for the simulation of flexible molecules with an arbitrary topology of Lennard-Jones and/or Gay-Berne sites. Computer Physics Communications 134(1): 23-32.
- M.J. CookM.R. Wilson (2001). A molecular dynamics simulation study of dipole correlation in the isotropic phase of the mesogens me5NF and GGP5CI. Molecular Crystals and Liquid Crystals 357: 127-+.
- M.J. CookM.R. Wilson (2001). Development of an all-atom force field for the simulation of liquid crystal molecules in condensed phases (LCFF). Molecular Crystals and Liquid Crystals 357: 149-165.
- D. J. Earl & J. IlnytskyiM. R. Wilson (2001). Computer simulations of soft repulsive spherocylinders. Molecular Physics 99(20): 1719-1726.
- Wilson, M.R. & Cook, M.J. (2000). Calculation of helical twisting power for liquid crystal chiral dopants. Journal of Chemical Physics 122: 1560-1564.
- Wilson, M.R., McBride, C. & Howard, J.A.K. (1998). Molecular dynamics simulation of liquid crystal phases using atomistic potentials. Molecular Physics 93(6): 955-964.
- Wilson, M.R. (1997). Molecular Dynamics Simulations of Flexible Liquid Crystal Molecules Using a Gay Berne/Lennard-Jones Model. Journal of Chemical Physics 107: 8654-8663.
- Wilson, M.R. (1996). Molecular modelling of liquid crystal systems: An internal coordinate Monte Carlo approach. Liquid Crystals 21: 437-447.